Semiconcave functions, Hamilton-Jacobi e
✍ Piermarco Cannarsa, Carlo Sinestrari
📂 Library
📅 2004
🏛 Birkhäuser Boston
🌐 English
✦ LIBER ✦
📁
Semiconcave Functions, Hamilton—Jacobi Equations, and Optimal Control
✍ Scribed by Piermarco Cannarsa, Carlo Sinestrari (auth.)
- Publisher
- Birkhäuser Basel
- Year
- 2004
- Tongue
- English
- Leaves
- 310
- Series
- Progress in Nonlinear Differential Equations and Their Applications 58
- Edition
- 1
- Category
- Library
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✦ Synopsis
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton–Jacobi equations.
The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.
A central role in the present work is reserved for the study of singularities. Singularities are first investigated for general semiconcave functions, then sharply estimated for solutions of Hamilton–Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems.
Researchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions. Graduate students will profit from this text as it provides a handy—yet rigorous—introduction to modern dynamic programming for nonlinear control systems.
✦ Table of Contents
A Model Problem....Pages 1-28
Semiconcave Functions....Pages 29-47
Generalized Gradients and Semiconcavity....Pages 49-76
Singularities of Semiconcave Functions....Pages 77-96
Hamilton-Jacobi Equations....Pages 97-139
Calculus of Variations....Pages 141-183
Optimal Control Problems....Pages 185-228
Control Problems with Exit Time....Pages 229-271
✦ Subjects
Partial Differential Equations; Measure and Integration; Optimization
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Semiconcave Functions, Hamilton-Jacobi E
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This text details the theory of semiconcave functions and describes the role they play in optimal control and Hamilton-Jacobi equations. Part I covers the general theory, summarizing and illustrating key results with significant examples. Part II is devoted to applications concerning the Bolza probl
Semiconcave Functions, Hamilton—Jacobi E
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🌐 English
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